 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dspt01()

 subroutine dspt01 ( character UPLO, integer N, double precision, dimension( * ) A, double precision, dimension( * ) AFAC, integer, dimension( * ) IPIV, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) RWORK, double precision RESID )

DSPT01

Purpose:
``` DSPT01 reconstructs a symmetric indefinite packed matrix A from its
block L*D*L' or U*D*U' factorization and computes the residual
norm( C - A ) / ( N * norm(A) * EPS ),
where C is the reconstructed matrix and EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.``` [in] AFAC ``` AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2) The factored form of the matrix A, stored as a packed triangular matrix. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block L*D*L' or U*D*U' factorization as computed by DSPTRF.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from DSPTRF.``` [out] C ` C is DOUBLE PRECISION array, dimension (LDC,N)` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )```

Definition at line 109 of file dspt01.f.

110 *
111 * -- LAPACK test routine --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 *
115 * .. Scalar Arguments ..
116  CHARACTER UPLO
117  INTEGER LDC, N
118  DOUBLE PRECISION RESID
119 * ..
120 * .. Array Arguments ..
121  INTEGER IPIV( * )
122  DOUBLE PRECISION A( * ), AFAC( * ), C( LDC, * ), RWORK( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION ZERO, ONE
129  parameter( zero = 0.0d+0, one = 1.0d+0 )
130 * ..
131 * .. Local Scalars ..
132  INTEGER I, INFO, J, JC
133  DOUBLE PRECISION ANORM, EPS
134 * ..
135 * .. External Functions ..
136  LOGICAL LSAME
137  DOUBLE PRECISION DLAMCH, DLANSP, DLANSY
138  EXTERNAL lsame, dlamch, dlansp, dlansy
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL dlaset, dlavsp
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC dble
145 * ..
146 * .. Executable Statements ..
147 *
148 * Quick exit if N = 0.
149 *
150  IF( n.LE.0 ) THEN
151  resid = zero
152  RETURN
153  END IF
154 *
155 * Determine EPS and the norm of A.
156 *
157  eps = dlamch( 'Epsilon' )
158  anorm = dlansp( '1', uplo, n, a, rwork )
159 *
160 * Initialize C to the identity matrix.
161 *
162  CALL dlaset( 'Full', n, n, zero, one, c, ldc )
163 *
164 * Call DLAVSP to form the product D * U' (or D * L' ).
165 *
166  CALL dlavsp( uplo, 'Transpose', 'Non-unit', n, n, afac, ipiv, c,
167  \$ ldc, info )
168 *
169 * Call DLAVSP again to multiply by U ( or L ).
170 *
171  CALL dlavsp( uplo, 'No transpose', 'Unit', n, n, afac, ipiv, c,
172  \$ ldc, info )
173 *
174 * Compute the difference C - A .
175 *
176  IF( lsame( uplo, 'U' ) ) THEN
177  jc = 0
178  DO 20 j = 1, n
179  DO 10 i = 1, j
180  c( i, j ) = c( i, j ) - a( jc+i )
181  10 CONTINUE
182  jc = jc + j
183  20 CONTINUE
184  ELSE
185  jc = 1
186  DO 40 j = 1, n
187  DO 30 i = j, n
188  c( i, j ) = c( i, j ) - a( jc+i-j )
189  30 CONTINUE
190  jc = jc + n - j + 1
191  40 CONTINUE
192  END IF
193 *
194 * Compute norm( C - A ) / ( N * norm(A) * EPS )
195 *
196  resid = dlansy( '1', uplo, n, c, ldc, rwork )
197 *
198  IF( anorm.LE.zero ) THEN
199  IF( resid.NE.zero )
200  \$ resid = one / eps
201  ELSE
202  resid = ( ( resid / dble( n ) ) / anorm ) / eps
203  END IF
204 *
205  RETURN
206 *
207 * End of DSPT01
208 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dlavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
DLAVSP
Definition: dlavsp.f:130
double precision function dlansp(NORM, UPLO, N, AP, WORK)
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansp.f:114
double precision function dlansy(NORM, UPLO, N, A, LDA, WORK)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansy.f:122
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